• 호남수학학술지
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• 제37권4호
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• pp.423-429
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• 2015

Dirichlet series is a Riemann zeta function attached with an arithmetic function. Here, we studied the properties of Dirichlet series and found some identities between arithmetic functions.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.443-450
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• 2016

In this paper we give some properties, explicit formulas, several identities, a connection with tangent numbers and polynomials, and some integral formulas.

• 대한수학회논문집
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• 제29권2호
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• pp.239-255
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• 2014

We develop a set of identities for Euler type sums. In particular we investigate products of shifted harmonic numbers of order two and reciprocal binomial coefficients.

• 대한수학회지
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• 제47권2호
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• pp.409-424
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• 2010

We express Gauss sums for symplectic and orthogonal groups over finite fields as averages of exponential sums over certain maximal tori. Together with our previous results, we obtain some interesting identities involving various classical Gauss and Kloosterman sums.

• 대한수학회보
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• 제55권1호
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• pp.107-114
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• 2018

In this paper, we give some identities for the higher-order Euler functions arising from the Fourier series of them. In addition, we investigate some formulae related to Bernoulli functions which are derived from our identities.

• East Asian mathematical journal
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• 제33권3호
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• pp.291-293
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• 2017

We aim to present two identities which reveal certain interesting relationships among three fundamental theta functions arising from the Jacobi's triple product in an elementary way.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.451-461
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• 2012

B.C. Berndt has established many relations between various infinite series using a transformation formula for a large class of functions, which comes from a more general class of Eisenstein series. In this paper, continuing his study, we find some infinite series identities.

• 대한수학회지
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• 제51권2호
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• pp.225-238
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• 2014

We apply modular function theory to find the relation among t-core partitions. By using the generators of function field corresponding to a certain modular group, we reprove the identities in [1] because their relations are linear for t = 3 or 5.

• 대한수학회보
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• 제52권6호
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• pp.2001-2010
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• 2015

In this paper, we give explicit and new identities for the Bernoulli numbers of the second kind which are derived from a non-linear differential equation.

• 대한수학회논문집
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• 제33권4호
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• pp.1239-1248
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• 2018

Recently, many authors have obtained several hypergeometric identities involving hypergeometric functions of one and multi-variables such as the Appell's functions and Horn's functions. In this paper, we obtain several new transformations suitably by applying the fractional calculus operator to these hypergeometric identities, which was introduced recently by Tremblay.